Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions

<table class="table-group" id="tab1"><tr><td><table class="table"><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr class="thead"><td class="align_left">Bimodality coefficient</td><td class="align_center">Hartigan’s dip statistic</td></tr><tr><td class="thead-hr" colspan="2"><hr/></td></tr><tr><td class="align_left">Deterministic result</td><td class="align_center">Probabilistic result according to significance level</td></tr><tr><td class="align_left">Third and fourth statistical moments</td><td class="align_center">Dip statistic</td></tr><tr><td class="align_left">Sensitive to third and fourth moments</td><td class="align_center">Does not depend on third and fourth moments</td></tr><tr><td class="align_left">Type I error</td><td class="align_center">Type II error</td></tr><tr><td class="align_left">Inconsistency</td><td class="align_center">Consistency</td></tr><tr><td class="align_left">Quick convergence</td><td class="align_center">Slow convergence</td></tr><tr class="table-tr"><td colspan="2"><hr class="tbody-hr"/></td></tr></table></td></tr><tr class="table-fn"><td><div><i>H</i><sub>0</sub>: <i>X</i> is a unimodal distribution.<br/></div></td></tr></table>

<div>Comparison between BC and HDS.</div>

Mathematical Problems in Engineering

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Table 1

Table 1: Development of Hartigan’s Dip Statistic with Bimodality Coefficient to Assess Multimodality of Distributions 